In addition to LilianaB's suggestion, there are a couple of stock English phrases appropriate in this kind of context: "in the clothes they stood up in" (sentence stress on the bolded words), as here:

"The slavery of poverty is frightful; I have studied it in all its aspects, having lived for years with men who have escaped from political shipwrecks in the clothes they stood up in." (source - Toronto Slavic Quarterly)

Or "with just the clothes on their back", as here:

"The family of five have been left with just the clothes on their back and what items they could squeeze into the boot of their car after the bush fire at Mount Forest Road destroyed their home on Tuesday." (source - Sydney Morning Herald)

Thanks for your answers. What I still don't quite understand is whether "в чем были" is a fixed expression in Russian, or there is some grammatical construction in this sentence which I don't get. In general, В чем быть = not to have any clothes other than those one is wearing? Could you be so kind as to give me other examples containing this word combination?

Thanks for your answers. What I still don't quite understand is whether "в чем были" is a fixed expression in Russian ... No it isn't a fixed expression. It's one way of saying someone is wearing something, so: Она была в черном платье - she was wearing a black dress.

In general, В чем быть = not to have any clothes other than those one is wearing?

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Not quite. It means one has got to bear the exact same clothes he or she was bearing before. For example: «Все они сразу же высыпали на улицу в чём были — кто в халате, а кто и прямо в трусах». The unfortunate passengers will have to wear the same clothes for a very long time, it is understood from the context. The 'they' from the above example were just in a hurry, it was their (quite likely not very fortunate) decision to skip out in whatever clothes were on them. Overall, the expression does have a shade of 'unfortunateness' in it. The sentiment of the verb «высыпали» rather suggest the hurry was not out of a serious danger or something, more likely it was some kind of amusement.

Could you be so kind as to give me other examples containing this word combination?

What I still don't quite understand is whether "в чем были" is a fixed expression in Russian, or there is some grammatical construction in this sentence which I don't get. In general, В чем быть = not to have any clothes other than those one is wearing? Could you be so kind as to give me other examples containing this word combination?

What I still don't quite understand is whether "в чем были" is a fixed expression in Russian, [...]

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In a sense, yes. You may think of this phrase as an idiom. I believe it is a short form where the word "clothes" has been omitted:
Многие из них в чем были [одеты], без всякого багажа, [в том и] попали на корабль, который отправлялся из Ялты или из Одессы.

Another idiom would be: "в чём мать родила" = "in the nuddy".

There is one similar construction: "как <state>, так и <action>", which means that the person started performing the action in a hurry and didn't have time to change his state (whatever it was).